A measurement of the forward-backward asymmetry of e⁺e⁻→bb by applying a jet charge algorithm to lifetime tagged events

Abstract

The forward-backward asymmetry of$e^ + e^ - \to Z^0 \to b\bar b$ has been measured using approximately 2.15 million hadronicZ ⁰ decays collected at the LEP e⁺e⁻ collider with the OPAL detector. A lifetime tag technique was used to select an enriched$b\bar b$ event sample. The measurement of the$b\bar b$ asymmetry was then performed using a jet charge algorithm to determine the direction of the primary quark. Values of:

$$\begin{gathered} A_{FB}^b = 0.062 \pm 0.034 \pm 0.002 - 0.082\Delta (\Gamma _{b\bar b} /\Gamma _{had} ) \hfill \\ at\sqrt s = 89.52GeV, \hfill \\ A_{FB}^b = 0.0963 \pm 0.0067 \pm 0.0038 - 0.471\Delta (\Gamma _{b\bar b} /\Gamma _{had} ) \hfill \\ at\sqrt s = 91.25GeV, \hfill \\ A_{FB}^b = 0.172 \pm 0.028 \pm 0.007 - 0.055\Delta (\Gamma _{b\bar b} /\Gamma _{had} ) \hfill \\ at\sqrt s = 92.94GeV, \hfill \\ \end{gathered}$$

were measured where, in each case, the first error is statistical, the second is systematic and the third term gives the variation due to a change$\Delta (\Gamma _{b\bar b} /\Gamma _{had} )$ in the value of$\Gamma _{b\bar b} /\Gamma _{had} = 0.216$ assumed. The dependence on the assumed charm asymmetry at the same energy is Δ(A ^b_FB )≈+0.07Δ(A ^c_FB ). Assuming the Standard Model form for the couplings, these measurements correspond to an effective weak mixing angle of:

$$\sin ^2 \theta _W^{eff,e} = 0.2313 \pm 0.0012 \pm 0.0006$$

giving M_top=196 ⁺³³⁺¹⁶₋₃₈₋₁₉ GeV/c ², where the first error is statistical and the second is systematic. The Higgs mass assumed is 300 GeV/c ². A variation in the assumed mass of the Higgs boson between 60 and 1000 GeV/c ² corresponds to an uncertainty in sin²θ ^eff,e_W of ±0.00006 and on M_top of ⁺²⁰₋₂₆ GeV/c ².